I've just found a way to get into Falgabard and get out as well.

1. Get Nautilus to dive into Saronia Continent.
2. Make it so you come up in the mountains surrounding Falgabard, don't woory, you can fly in them for now.
3. Land from the North(easier) so that you walk on the grass, but can still enter the Nautilus in the mountains.
4. When your're done get in the Nautilus and fly off the mountains.